## First-order P-wave ray synthetic seismograms
in inhomogeneous weakly anisotropic media

**Ivan Psencik** and
**Veronique Farra**
### Summary

We propose approximate equations for P-wave ray-theory Green function
for smooth inhomogeneous weakly anisotropic media. Equations are
based on perturbation theory, in which deviations of anisotropy from
isotropy are considered to be the first-order quantities. For evaluation
of the approximate Green function, earlier derived first-order
ray-tracing equations and in this paper derived first-order
dynamic-ray-tracing equations are used.

The first-order ray-theory P-wave Green function for inhomogeneous,
weakly anisotro-pic media of arbitrary symmetry depends, at most, on
15 weak-anisotropy parameters. For anisotropic media of higher-symmetry
than monoclinic,
all equations involved differ only slightly from the corresponding
equations for isotropic media. For vanishing anisotropy, the equations
reduce to equations for computation of standard ray-theory Green
function for isotropic media. These properties make the proposed
approximate Green function an easy and natural substitute of traditional Green
function for isotropic media.

Numerical tests for configuration and models used in seismic
prospecting indicate negligible dependence of accuracy of the
approximate Green function on inhomogeneity of the medium. Accuracy
depends more strongly on strength of anisotropy in general and
on angular variation of phase velocity due to anisotropy in particular.
For example, for anisotropy of about 8 %, considered in the
examples presented, the relative errors of
the geometrical spreading are usually under 1 %; for anisotropy of
about 20 %, however, they may locally reach as much as 20 %.

### Keywords

Inhomogeneous media, perturbation methods, P waves,
seismic anisotropy, seismic ray theory, synthetic seismograms.

### Whole paper

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In: Seismic Waves in Complex 3-D Structures, Report 17,
pp. 111-134, Dep. Geophys., Charles Univ., Prague, 2007.

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